General Discussion of Aerodynamic Focusing
Aerodynamic Focusing using an Aerodynamic Lens
The use of aerodynamic lenses to focus an aerosol stream was first reported by Lui. An aerodynamic lens can be defined as a flow configuration in which a stream traveling through a cylindrical channel with diameter D is passed through an orifice with diameter d, undergoing one contraction upstream of the orifice and one subsequent and immediate expansion downstream of the orifice. A contraction of an aerosol stream is produced as the flow approaches and passes through the orifice. The gas then undergoes an expansion as the flow propagates downstream into a wider cross sectional area. Flow through the orifice forces particles towards the flow axis, so that the aerosol stream is narrowed and collimated. Aerosol streams collimated by an aerodynamic lens system have been designed for use in many fields, including pharmaceutical aerosol delivery and additive manufacturing. In the typical aerodynamic lens system, an aerosol stream is tightly confined around the axis of a flow cell by passing the particle distribution through a series of axisymmetric contractions and expansions. Each section of the lens system consisting of a flow channel and an orifice is defined as a stage. Lui has presented a method and apparatus for focusing sub-micron particles using an aerodynamic lens system. Di Fonzo et. al. and Dong et. al. have designed lens systems that focused particles with diameters in the range from 10 to 100 nanometers and 10 to 200 nanometers, respectively. Wang has designed a lens system to focus particles in the range of 3 to 30 nanometers. Lee has reported a method of focusing micron-sized particles at atmospheric pressures using a single lens system composed of multiple stages.
In U.S. Pat. No. 6,348,687, Brockmann discloses an apparatus for generating a collimated aerosol beam of particles with diameters from 1 to 100 microns. The aerodynamic lens system of Brockmann uses a series of fixed lens and an annular sheath gas surrounding a particle-laden carrier gas. The system of Brockmann was used to focus 15 micron aluminum particles to a diameter of 800 microns, and generally uses the same aerosol and sheath gas flow rates. Lee (U.S. Pat. No. 7,652,247) discloses an aerodynamic lens system for focusing nanoparticles in air with diameters between 5 and 50 nanometers. In U.S. Pat. No. 8,119,977, Lee discloses a multi-stage, multi-orifice aerodynamic lens for focusing a range of particle diameters covering two orders of magnitude, from 30 to 3000 nanometers. In U.S. Pat. No. 6,924,004, Rao discloses a method and apparatus for depositing films and coatings from a nanoparticle stream focused using an aerodynamic lens system. The apparatus of Rao uses high-speed impaction to deposit nanoparticles on a substrate. A method of separating particles from a gas flow using successive expansions and compressions of the flow created by an aerodynamic lens is discussed by Novosselov in U.S. Pat. No. 8,561,486.
The preferred embodiment of the invention is shown in FIG. 1. The apparatus consists of an ultrasonic atomizer (1), a pulsed power source (9), a flow cell (2), and an aerodynamic lens assembly (3), and (4). The pulsed power source produces a constant aerosol density in the atomizer, applying a voltage pulse to the transducer (13) at intervals ranging from approximately 0.5 to 2 seconds. The aerodynamic lens assembly focuses the distribution of aerosol droplets at a point approximately three to ten millimeters downstream of the second lens (4), enabling accurate printing of various inks, including nanoparticle suspensions, precursor solutions, and polymer is solutions.
Cross sectional representations of various aerodynamic configurations are shown in FIG. 2. In general, each configuration consists of an orifice or series of orifices connected to a converging exit nozzle with a sheathed gas flow. FIG. 2a shows a configuration wherein an aerosol stream emerges from a capillary 13 and flows into a sheathed exit nozzle 15. FIG. 2b shows an aerosol stream that is first collimated by an aerodynamic lens 14 before passing through a sheathed exit nozzle 15. In FIG. 2c an aerosol stream emerges from a capillary 13 and enters a sheathed aerodynamic lens 16 mounted inside an interchangeable exit nozzle 15. FIG. 2d shows a system of two aerodynamic lenses in communication with a converging exit nozzle. The aerosol stream of FIG. 2d is sheathed after passing from the first lens 17, and during passage through the second lens 16. The configurations of FIGS. 2c through 2d are used in the present invention. In each configuration, the converging exit nozzle may be replaced by an orifice with a non-converging flow cross section.
Aerodynamic Focusing using a Single-Orifice
Numerous studies have been performed to characterize the focusing effect created by propagating an aerosol stream through a single orifice consisting of a capillary tube, a converging nozzle, or a sheathed nozzle. (Dahneke, 1977), (Dahneke, 1978), (Cheng and Dahneke, 1979), (Dahneke, 1979), (Mallina, 1999), (Mallina, 2000). These theoretical and experimental studies conclude that single-orifice systems can only focus a narrow range of particle sizes to a sharp point (Deng, 2008). Specifically, single-orifice systems can focus a mono-dispersed aerosol distribution to a well-defined point, but poly-dispersed distributions will be focused at different positions along the flow axis, with the focus position and focused diameter dependent on the droplet size. A mathematical description of focusing of an aerosol stream passing through an orifice has been developed in terms of a critical Stokes number S*. (De la Mora, 1988). Particles with Stokes number above S* cross the flow axis at some finite distance from the lens, while sub-critical particles do not cross the axis, and critical particles cross the axis at infinity.
In U.S. Pat. No. 4,019,188, Hochberg discloses an apparatus for producing a narrow, collimated stream of aerosol particles using a carrier gas jet and a surrounding sheath flow. The Hochberg apparatus uses a carrier gas velocity that forces particles to the center of the gas flow, surrounds the flow with a sheath gas, and directs the combined flow through a nozzle.
Aerodynamic Focusing for Direct Printing Applications
In a Direct Printing technique, a liquid is deposited onto a substrate without the use of masks or lithographic techniques. The present invention uses an aerodynamic lens system to form a thin aerosol jet surrounded by a sheath gas. The diameter of the core aerosol distribution is a function of the lens parameters such as channel length, lens orifice diameter, and the length of the lens.
The present invention discloses a method for stable, maskless direct printing on a substrate using aerodynamic focusing to produce highly collimated beams of sub-micron and micron-size droplets using an aerodynamic lens system and an annular sheath flow closely matched to the output of an aerosol source. In the preferred embodiment of the invention, the aerosol source is a low-power ultrasonic atomizer operating in a continuous or pulsed mode. The atomizer described herein produces a relatively narrow range of droplet diameters, from approximately 0.5 to 5 microns, facilitating the production of a narrow, collimated aerosol beam. The atomizer power is typically less than approximately 10 watts. The lens system may consist of a single stage or multiple stages. The present invention is used to deposit well-defined traces onto various substrates with sub-micron edge definition. The apparatus uses interchangeable and variable aerodynamic lens assemblies with configurations that can be tuned to match the aerosol output of the aerosol generator, so that a high degree of collimation of the aerosol beam is obtained. Tuning the atomizer/aerodynamic lens assembly is achieved by varying the lens diameters or by varying the distance between the lenses.
Atomization and Aerodynamic Lens Selection
The atomization method and the resulting droplet distribution are of critical importance in aerosol-based deposition processes. Aerosol droplet diameters that are useful for direct write applications are generally in the range of approximately 1 to 5 microns. However production of mono-dispersed aerosols in the range of 1 to 5 microns can be prone to clogging and unstable droplet generation. Consequently, aerosol generators with a relatively wide droplet distribution are commonly used in many aerosol-based applications. If a poly-dispersed aerosol droplet distribution is used however, poor deposition quality may be obtained unless the deposition system provides a mechanism for collimation or focusing of a range of droplet sizes. It is the object of the present invention to provide apparatuses and methods for deposition of fine traces on various substrates using a closely-matched atomizer/aerodynamic lens assembly.
Mono-Dispersed Aerosol Generation
Several mono-dispersed aerosol generators are commercially available. Chen provides a list of commercially available mono-dispersed aerosol generators, with information on droplet size, liquid type, carrier gas, and application. One method of producing a mono-dispersed aerosol distribution is by controlling the breakup of a liquid jet propagated from an orifice. Controlled droplet breakup of a liquid jet is used to produce mono-dispersed droplets in the range from 1 to 1000 microns. Similarly mono-dispersed aerosols have been produced by applying a pressure pulse to a liquid volume in direct communication with an orifice. While mono-dispersed aerosol generation devices are commercially available, the application of such devices is largely found in research settings and is not widely found in production environments. An object of the present invention is therefore the provision of a direct write apparatus and method using a poly-dispersed aerosol source.
Poly-Dispersed Aerosol Generation
A common method of producing an aerosol of liquid droplets is to use piezoelectric excitation of a bulk liquid in contact with an ultrasonic transducer. The liquid may be placed in direct contact with the transducer, or the liquid may be held in a secondary container, with the ultrasonic energy transmitted to the liquid through a thin membrane. Direct contact methods generally require less power for atomization, since no transmission losses occur between the transducer and membrane. In ultrasonic atomization a fluid spout accompanies the production of aerosol, and may extend several centimeters above the surface of the transducer. Furthermore, studies have shown that the ultrasonic atomization process described above produces a distribution of droplets with diameters of approximately 0.5 to 10 microns.
The mean droplet diameter of an ultrasonic distribution is related to the liquid surface tension and viscosity and the frequency of the ultrasonic vibration according to equation 1,
                    D        =                  0.34          ⁢                                    (                                                8                  ⁢                  πγ                                                  ρ                  ⁢                                                                          ⁢                                      f                    2                                                              )                                      1              3                                                  1      
where γ is the surface tension, ρ is the density, and f the excitation frequency. Substituting for the liquid properties and a drive frequency of 1.6 MHz yields a mean droplet diameter of approximately 2.6 microns. The aerodynamic lens system of the invention therefore provides at least one aerodynamic lens to focus droplets with diameters of approximately 2.5 microns. Droplet diameters that fall outside the region of approximately 2.5±2 microns are focused by the sheath gas as the aerosol stream passes through a second lens, or through a series of lenses and an exit nozzle.
Pulsed Aerosol Generation
With reference to FIG. 1, one embodiment of the present invention uses a pulsed power source 9 to drive a piezoelectric transducer 13 of an ultrasonic atomizer unit 1. The power circuit provides excitation of the transducer at variable frequencies in the range of approximately 1 to 2 MHz. Pulsed operation of the atomizer provides generation of a dense, saturated aerosol suspension within the atomizer. The pulsed operation allows for stable aerosol delivery to the flow cell, and reduces or eliminates the production of large droplets that can be entrained in the flow channels of the atomizer or flow cell.